First we break down the initial velocity into its horizontal and vertical components:
We know that the acceleration in the horizontal component is 0, it is a constant velocity. Meanwhile in the vertical component we have an acceleration of
The rate of change of horizontal position is constant (it changes
The velocity of horizontal position doesn't change, which means it's constant.
AKA the rate of change of the rate of change of the horizontal position is 0(velocity never changes):
The actual formula for x axis:
This is just the formula for Non-Accelerated Linear Motion.
The vertical position changes
The rate of change of vertical position is not constant because the gravitational pull gets bigger over time:
The rate of change of vertical position also changes because of acceleration, it changes
The actual formula for
This is just the formula for Accelerated Linear Motion, where the acceleration is gravity.
The following equation tells us at
Horizontal motion equation
Vertical motion equation
Solving the horizontal motion equation for time
Now we can plug this into the vertical motion equation, basically its like putting in the formula the time
Substituting
Expanding and simplifying the equation
Substituting
Isn't it just better to compute the fucking time and plug it in directly? instead of using this shit giant formula?
This is just the velocity multiplied by time to obtain how much we traveled in that time.
The time is the time of arrival(or time at which the object reaches the ground), which we compute as: